Abstract: Entropy and its various generalizations are widely used in mathematical statistics, communication theory, physical and computer sciences for characterizing the amount of information in a probability distribution. We consider estimators of the quadratic Rényi entropy and some related characteristics of discrete and continuous probability distributions based on the number of coincident ...

We propose a quartic function to represent a family of continuous quality loss functions. Depending on the choice of its parameters the shape of this function within the specification limits can be either symmetric or asymmetric, and it can be either similar to the ubiquitous quadratic loss function or somewhat closer to the conventional step function. We examine this family of loss functions i...

This paper introduces IQPs (Integer Quadratic Programs) as a way to model joint inference for the task of concept recognition in clinical domain. IQPs make it possible to easily incorporate soft constraints in the optimization framework and still support exact global inference. We show that soft constraints give statistically significant performance improvements when compared to hard constraints.

In the present paper we outline the stochastic limit approach to superfluidity. The Hamiltonian describing the interaction between the Bose condensate and the normal phase is introduced. Sufficient in the stochastic limit condition of superfluidity is proposed. Existence of superfluidity in the stochastic limit of this system is proved and the non– linear (quadratic) equation of motion describi...

Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.

Let A„{a, b) = {ban+(a-l)/b)2+4an with n > 1 and ¿>|a-l . If W is a finite set of primes such that for each n > 1 there exists some q £W for which the Legendre symbol {A„{a, b)/q) ^ -1 , we call <£ a quadratic residue cover (QRC) for the quadratic fields K„{a, b) = Q{^jA„{a, b)). It is shown how the existence of a QRC for any a, b can be used to determine lower bounds on the class number of K„{...

Merging data from multiple studies has been widely adopted in biomedical research. In this paper, we consider two major issues related to merging longitudinal datasets. We first develop a rigorous hypothesis testing procedure to assess the validity of data merging, and then propose a flexible joint estimation procedure that enables us to analyse merged data and to account for different within-s...

Generalized estimating equations (GEE) are commonly employed for the analysis of correlated data. However, the quadratic inference function (QIF) method is increasing in popularity because of its multiple theoretical advantages over GEE. We base our focus on the fact that the QIF method is more efficient than GEE when the working covariance structure for the data is misspecified. It has been sh...